A tissue is a geometrical, space-filling, random cellular network; it remains in this steady state while individual cells divide. Cell division is a local, elementary topological transformation which establishes statistical equilibrium of the structure. We describe the physical conditions to maintain stationary the epidermis (of mammals or of the cucumber), in spite of the fact that cells constantly divide and die. Specifically, we study the statistical equilibrium of the basal layer, a corrugated surface filled with cells, constituting a (...) two-dimensional topological froth. Cells divide and detach from the basal layer, and these two topological transformations are responsible for the stationary state of the epidermis. The topological froth is capable of responding rapidly and locally to external constraints, and is a good illustration of the plasticity of random cellular networks.Statistical equilibrium is controlled by entropy, both as a measure of disorder and as information, and is characterized by observable relations between average cell shapes and sizes. The technique can be applied to any random cellular network in dynamical equilibrium. Mitosis as the dominating topological transformation and the fact that the distribution of cell shapes is very narrow are the only inputs specific to biology. (shrink)

A complete theoretical model describing artificial disintegration of nuclei by bombardment with α-particles, developed by Majorana as early as 1930, is discussed in detail jointly with the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear (...) process, which is the directly measurable quantity of interest in the experiments. Although this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana work anticipates by several years the related seminal paper by Fano on Atomic Physics. (shrink)

This study examines John Stuart Mill’s philosophy of history and his efforts to develop a comprehensive methodology for the social sciences. The author argues that Mill’s interpretation of history and his conception of cultural and economic stationary states were central to his critique of mass culture and his advocacy of individual autonomy.

A simple stationary state is set up by combining the two de Broglie waves from two particles traveling in one direction with equal and opposite velocities. By considering the waves forming this state from the point of view of all possible observers moving in the same direction, it is shown that the basic standing wave pattern does not alter, but that the particle will be confined to a small region stationary relative to this pattern. This region (...) is similar in extent to that confining a free particle, the natural internal frequency of the particle being raised. This agrees with previous suggestions that a particle in a stationary state without angular momentum is stationary. (shrink)

In his evaluation of the major social reform movements of his era, Mill chastised well-meaning reformers for their reluctance to elevate Malthusianism to a position of prominence in their efforts. He was convinced that the key to the material, mental, and moral improvement of the poor and the workers lay in a reduction of their physical numbers and in the behavioural modifications entailed by such a diminution, whereas most other reformers looked elsewhere for solutions. A favourite assumption about the proper (...) means for effecting social reform was that economic growth served as an effective and almost automatic instrument for improving society. Then, as now, an unquestioned faith in the capacity of a progressive economy to stimulate gains in per capita income for the lower classes set the terms for the discussion.1 However, by suggesting that broader and more intensive economic development without a corresponding reduction in the rate of population increase would not generate material gains for those living in indigence, let alone the broader socio-cultural progress that was to have followed closely upon its heels, Mill casts aspersions upon the ‘false ideal’ of economic growth which informed many grand programmes for social progress. (shrink)

In this study, the authors utilize mountain pass lemma, variational methods, regularization technique, and the Lyapunov function method to derive the unique existence of the positive classical stationary solution of a single-species ecosystem. Particularly, the geometric characteristic of saddle point in the mountain pass lemma guarantees that the equilibrium point is the ground state stationary solution of the ecosystem. Based on the obtained uniqueness result, the authors use the Lyapunov function method to derive the globally exponential stability (...) criterion, which illuminates that under some suitable conditions, a certain internal competition is conducive to the global stability of the population, and a certain amount of family planning is conducive to the overall stability of the population. Most notably, the regularity technique of weak stationary solution employed in this study can also be applied to some existing literature related with time-delays reaction-diffusion systems for the purpose of regularization of weak solutions. Finally, an illuminative numerical example shows the effectiveness of the proposed methods. (shrink)

By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac’s theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a quantum dynamics of a single relativistic fermion, and its solution is reduced to solution of the generalized Pauli equation for two quasiparticles which move in the Euclidean space with their effective masses holding information about the Lorentzian symmetry of the four-dimensional space-time. We reveal the (...) correspondence between the Dirac bispinor and Pauli spinor , and show that all four components of the Dirac bispinor correspond to a fermion . Mixing the particle and antiparticle states is prohibited. On this basis we discuss the paradoxical phenomena of Zitterbewegung and the Klein tunneling. (shrink)

The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0)within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic (...) equation with a free parameter h′ with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h′>0. The exact solutions for which h′<h are called sub-Heisenberg states. These nonperturbative solutions appear in the form of Gaussian, non-Heisenberg states for which the initial classical uncertainty relation takes the form 〈(δx 2)〉〈(δp) 2 〉=(h′/2) 2,which includes the limit of zero indeterminacy (h → 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy hΩ 0 /2 and 〈(δx) 2 〉〈(δp) 2 〉=h 2 /4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states. (shrink)

It is shown that the stationary states of stochastic systems are stable. Therefore one cannot use the stationary probability distributions for describing the stochastic systems in metastable states. It is shown that the nonstationary stochastic processes can have sample paths with stationary parts. It is proposed to consider these stationary parts as the metastable states.

Background: Patients in a vegetative state pose problems in diagnosis, prognosis and treatment. Currently, no prognostic markers predict the chance of recovery, which has serious consequences, especially in end-of-life decision-making. Objective: We aimed to assess an objective measurement of prognosis using advanced electroencephalography (EEG). Methods: EEG data (19 channels) were collected in 14 patients who were diagnosed to be persistently vegetative based on repeated clinical evaluations at 3 months following brain damage. EEG structure parameters (amplitude, duration and variability within (...) quasi-stationary segments, as well as the spatial synchrony between such segments and the strength of this synchrony) were used to predict recovery of consciousness 3 months later. Results: The number and strength of cortical functional connections between EEG segments were higher in patients who recovered consciousness (P < .05 – P < .001) compared with those who did not recover. Linear regression analysis confirms that EEG structure parameters are capable of predicting (P = .0025) recovery of consciousness 6 months post-injury, whereas the same analysis failed to significantly predict patient outcome based on aspects of their clinical history alone (P = .629) or conventional EEG spectrum power (P = .473). Conclusions: The result of this preliminary study demonstrates that structural strategy of EEG analysis is better suited for providing prognosis of consciousness recovery than existing methods of clinical assessment and of conventional EEG. Our results may be a starting point for developing reliable prognosticators in patients who are in vegetative state, with the potential to improve their day-to-day management, quality of life, and access to early interventions. (shrink)

After presenting the foundation and the basic equations of a new 5-dimensional projective unified field theory, the problem of incorporating spinor fields into this framework is investigated. Apart from Pauli's method, we propose a new approach which leads to a consistent 5-dimensional spinor theory with a series of physical consequences (variability of the 4-dimensional “rest mass,” instability of 4-dimensional “stationary states,” etc.).

We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary (...) states of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation. (shrink)

The current article aims to provide an up-to-date synopsis of available techniques to study affect dynamics using intensive longitudinal data (ILD). We do so by introducing the following eight dichotomies that help elucidate what kind of data one has, what process aspects are of interest, and what research questions are being considered: (1) single- versus multiple-person data; (2) univariate versus multivariate models; (3) stationary versus nonstationary models; (4) linear versus nonlinear models; (5) discrete time versus continuous time models; (6) (...) discrete versus continuous variables; (7) time versus frequency domain; and (8) modeling the process versus computing descriptives. In addition, we discuss what we believe to be the most urging future challenges regarding the modeling of affect dynamics. (shrink)

My aim in this article is to contribute to defences of working time policies by attempting to meet an objection that comes from those who condemn these measures on the alleged grounds that they reduce economic output. What is more, as I emphasize throughout, it is possible to rebut such a concern in a fashion that is consistent with the demands of liberal anti-perfectionism. In itself, this is a philosophically striking and politically significant result. However, beyond this, much of the (...) value of my discussion lies in the details of how to meet the relevant objection, and perhaps especially in my novel liberal defence of the ideal of the stationary state. (shrink)

The free-energy principle (FEP) builds on an assumption that sensor–motor loops exhibit Markov blankets in stationary state. We argue that there is rarely reason to assume a system's internal and external states are conditionally independent given the sensorimotor states, and often reason to assume otherwise. However, under mild assumptions internal and external states are conditionally independent given the sensorimotor history.

A stationary subset S of a regular uncountable cardinal κ reflects fully at regular cardinals if for every stationary set $T \subseteq \kappa$ of higher order consisting of regular cardinals there exists an α ∈ T such that S ∩ α is a stationary subset of α. Full Reflection states that every stationary set reflects fully at regular cardinals. We will prove that under a slightly weaker assumption than κ having the Mitchell order κ++ it is (...) consistent that Full Reflection holds at every λ ≤ κ and κ is measurable. (shrink)

The aim of this study is to present a stability in a two-dimensional dynamical system of endogenous growth with public capital. We assume the simple model of the economic growth, in which both private and public capital can influence on the rate of growth of knowledge. The public capital is rival but non excludable goods, i.e. there is a congestion in use of public capital. The model of growth is formulated as a two-dimensional dynamical system. Using mathematical methods of dynamical (...) systems, we analyze growth paths as well as the stationary states of the system and their stability. (shrink)

The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. The partitionAnsatz is then applied to the Dirac equation, where an exact partition into a continuity equation and a Hamilton-Jacobi equation is obtained.

The article discusses a new understanding of the reality in the 20th century. Since the key figure in these changes was the Danish physicist Niels Bohr, we refer to his early and later articles to analyze the use of the term “reality”. Through an analysis of the terms, it is shown that Bohr describes discoveries in earlier articles that are inconsistent with old concepts in physics, and it is these questions that will further lead him to a new understanding of (...) reality. In the article we also indicate how many times and in what contexts the term “reality” is used. Further, we find that the term “reality” is more common in later articles than in his earlier works. Through the analyzing of usage of certain terms, we show how the emphasis in the early and late Bohr’s articles shifts. For many years, the Danish physicist has sought to clarify quantum theory. In some later articles, we note that the problems affect not only physical, but also other areas of knowledge. We also analyze the use of the term in later articles. This analysis shows how Niels Bohr’s discoveries in the nature of the objects of the micro-world lead him to questions about the nature of reality. How discoveries in the microcosm affect the new conception of reality is best traced in controversy with other physicists. As the most striking example, we took the article “Discussion with Einstein on epistemological problems in atomic physics”. In this article, Bohr describes the specific behavior of micro-objects, features of physical experiments and proves the idea that a fundamentally new understanding of physical processes is needed. An analysis of the terms shows that, from Bohr’s point of view, reality itself is as described by its quantum mechanics. We strive to show the evolution of Bohr’s views in the context of how they influenced the revision of all physics. We conclude that the discovery of stationary states in an atom is the first step to rethinking philosophical questions of a nature of reality. (shrink)

Dirac's equation is reviewed and found to be based on nonrelativistic ideas of probability. A 4-space formulation is proposed that is completely Lorentzinvariant, using probability distributions in space-time with the particle's proper time as a parameter for the evolution of the wave function. This leads to a new wave equation which implies that the proper mass of a particle is an observable, and is sharp only in stationary states. The model has a built-in arrow of time, which is associated (...) with a restriction to positive-energy solutions. The usual solution for a Coulomb field is retained, though it now implies a slightly different charge distribution. The conventional nonstationary solutions become invalid. The new formulation appears to offer a resolution of difficulties that have been associated with Dirac's equation. It also predicts the occurrence of virtual pairs at a level that may be experimentally testable, and suggests a mechanism for self-cancellation of the vacuum energy. (shrink)

Using the position as an independent variable, and time as the dependent variable, we derive the function $${\mathcal{P}}^{(\pm )}=\pm \sqrt{2m({\mathcal{H}}-{\mathcal{V}}(q))}$$, which generates the space evolution under the potential $${\mathcal{V}}(q)$$ and Hamiltonian $${\mathcal{H}}$$. No parametrization is used. Canonically conjugated variables are the time and minus the Hamiltonian ( $$-{\mathcal{H}}$$ ). While the classical dynamics do not change, the corresponding Quantum operator $${{{\hat{\mathcal P}}}}^{(\pm )}$$ naturally leads to a 1/2-fractional time evolution, consistent with a recent proposed space–time symmetric formalism of the Quantum (...) Mechanics. Using Dirac’s procedure, separation of variables is possible, and while the two-coupled position-independent Dirac equations depend on the 1/2-fractional derivative, the two-coupled time-independent Dirac equations lead to positive and negative shifts in the potential, proportional to the force. Both equations couple the (±) solutions of $${{{\hat{\mathcal P}}}}^{(\pm )}$$ and the kinetic energy $${\mathcal{K}}_{0}$$ (separation constant) is the coupling strength. Thus, we obtain a pair of coupled states for systems with finite forces, not necessarily stationary states. The potential shifts for the harmonic oscillator (HO) are $$\pm {\hbar {\omega}} /2$$, and the corresponding pair of states are coupled for $${\mathcal{K}}_{0}\ne 0$$. No time evolution is present for $${\mathcal{K}}_{0}=0$$, and the ground state with energy $${\hbar {\omega}} /2$$ is stable. For $${\mathcal{K}}_{0}>0$$, the ground state becomes coupled to the state with energy $$-{\hbar {\omega}} /2$$, and this coupling allows to describe higher excited states in the HO. Energy quantization of the HO leads to the quantization of $${\mathcal{K}}_{0}=k{\hbar {\omega}}$$ ( $$k=1,2,\ldots$$ ). For the one-dimensional Hydrogen atom, the potential shifts become imaginary and position-dependent. Decoupled case $${\mathcal{K}}_{0}=0$$ leads to plane-waves-like solutions at the threshold. Above the threshold ( $${\mathcal{K}}_{0}>0$$ ), we obtain a plane-wave-like solution, and for the bounded states ( $${\mathcal{K}}_{0}<0$$ ), the wave-function becomes similar to the exact solutions but squeezed closer to the nucleus. (shrink)

This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. (...) A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of ) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis", which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4, and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided. (shrink)

With the wide adoption of social collaborative coding, more and more developers participate and collaborate on platforms such as GitHub through rich social and technical relationships, forming a large-scale complex technical system. Like the functionalities of critical nodes in other complex systems, influential developers and projects usually play an important role in driving this technical system to more optimized states with higher efficiency for software development, which makes it a meaningful research direction on identifying influential developers and projects in social (...) collaborative coding platforms. However, traditional ranking methods seldom take into account the continuous interactions and the driving forces of human dynamics. In this paper, we combine the bursty interactions and the bipartite network structure between developers and projects and propose the BurstBiRank model. Firstly, the burstiness between each pair of developers and projects is calculated. Secondly, a weighted developer-project bipartite network is constructed using the burstiness as weight. Finally, an iterative score diffusion process is applied to this bipartite network and a final ranking score is obtained at the stationary state. The real-world case study on GitHub demonstrates the effectiveness of our proposed BurstBiRank and the outperformance of traditional ranking methods. (shrink)

In this paper we study a classical and theoretical system which consists of an elastic medium carrying transverse waves and one point-like high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this system. Afterwards we always consider the case where the concretion is not the wave source any longer. Then the concretion obeys a general and covariant guidance formula, which leads in low-velocity approximation to an equivalent de (...) Broglie-Bohm guidance formula. The concretion moves then as if exists an equivalent quantum potential. A strictly equivalent free Schrödinger equation is retrieved, as well as the quantum stationary states in a linear or spherical cavity. We compute the energy of the concretion, naturally defined from the energy density of the vibrating elastic medium. Provided one condition about the amplitude of oscillation is fulfilled, it strikingly appears that the energy and momentum of the concretion not only are written in the same form as in quantum mechanics, but also encapsulate equivalent relativistic formulas. (shrink)

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an (...) analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect. (shrink)

Must we always pursue economic growth? Kogelmann answers yes. Not only should poor countries pursue growth, but rich countries should as well. Kogelmann aims to provide awealth-insensitive argument– one demonstrating all countries should pursue growth regardless of their wealth. His central argument – the no halting growth (NHG) argument – says no country experiencing growth should stop it, because doing so requires undermining the conditions causing it and those conditions are independently morally desirable, so they should not be undermined. For (...) countries not growing, he may argue that they have an obligation to implement the conditions that cause growth because they are independently morally desirable. Call this the implementation argument. I contend that neither argument is wealth-insensitive as each fails to establish an obligation to pursue growth. I attempt to diagnose how this could be and propose that it is a product of attempting to answer three questions about growth simultaneously. (shrink)

In this article I argue that if conscience, working properly, involves some form of ‘moral tug’, then this is incompatible with the state of ‘quiescence’ put forward as a central element of Eleonore Stump’s account of repentance. Quiescence is also a key notion for Stump’s theodicy in Wandering in the Darkness and Stump’s thesis in her book, Atonement. Quiescence is about an inactive, or neutral, or stationary, state of the will prior to turning to the good, or (...) God, through receiving God’s saving grace. But if God exerts a non–coercive pressure on people through their conscience to turn to him, and turn from evil, then this drawing towards the good, or tugging away from evil, can only be yielded to, or resisted. There is no neutral state. I give examples of language such as being ‘bound’ to obey one’s conscience, which seem to reflect such non–coercive pressure. I conclude by commenting on free will. (shrink)

While there had been much radical thought before John Stuart Mill, Joseph Persky argues it was Mill, as he moved to the left, who provided the radical wing of liberalism with its first serious analytical foundation, a political economy of progress that still echoes today. A rereading of Mill's mature work suggests his theoretical understanding of accumulation led him to see laissez-faire capitalism as a transitional system. Deeply committed to the egalitarian precepts of the Enlightenment, Mill advocated gradualism and rejected (...) revolutionary expropriation on utilitarian grounds: gradualism, not expropriation, promised meaningful long-term gains for the working classes. He endorsed laissez-faire capitalism because his theory of accumulation saw that system approaching a stationary state characterized by a great reduction in inequality and an expansion of cooperative production. These tendencies, in combination with an aggressive reform agenda made possible by the extension of the franchise, promised to provide a material base for social progress and individual development.The Political Economy of Progress goes on to claim that Mill's radical political economy anticipated more than a little of Marx's analysis of capitalism and laid a foundation for the work of Fabians and other gradualist radicals in the 20th century. More recently, modern philosophic radicals, such as Rawls, have deep links to this Millean political economy. These links are still worthy of development. In particular, a politically meaningful acceptance of Rawls's radical liberalism waits on a movement capable of re-engineering the workplace in a manner consistent with Mill's endorsement of worker management. (shrink)

This article (in Swedish) situates John Stuart Mill's normative discussion on 'stationary state' in contemporary sustainability categories.

A transient quantum effect is shown to occur for a superposition of stationary states. An alternative to Schrödinger's equation is considered which predicts a transient effect even for energy eigenstates.

John Stuart Mill is known as the first canonical Western philosopher to espouse a stationary state of economic growth, and as such he can be seen as an important totemic figure for reformist strategies in environmental ethics. However, his reputation among environmental thinkers has been rendered more ambiguous in recent years by increased attention to his essay “Nature.” The “Nature” essay has been much used lately by critics to oppose claims that independent nature may properly be seen as (...) important in any way as an ethical guide or inspiration, and that Mill’s philosophy may feasibly be viewed as pro-environmentalist. This use of Mill’s essay is mistaken, and has undermined appreciation of the potential significance of Mill’s thought for environmental philosophy. When examining the most detailed of the critical treatments of the essay, reading “Nature” as an anti-environmentalist text badly distorts the essay’s meaning by ripping it from the context of Mill’s intentions as well as from the very specific and significant historical circumstances and biographical conditions of its production. Attending properly to these factors shows that the essay is unrepresentative of Mill’s general position and rather philosophically weaker than its reputation. Reading the text as a definitive statement of Mill’s supposed anti-naturalism is thus mistaken and fails to recognize different modes and significances in “following nature,” some of which Mill supported. The “Nature” essay is an aberrant outlier in the Mill canon, and one which should no longer be allowed to undermine Mill’s strong and important environmentalist credentials. (shrink)

The Einstein-de Broglie soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. It is shown that the electron-solilon center travels along some stationary orbit around the Coulomb center. The electromagnetic radiation is absent as the Poynting vector has non-wave asymptote O(r −3)after averaging over angles.

A dynamic systemS P described by the Pauli equation for nonrelativistic electron is investigated merely as a distributed dynamic system. No quantum principles are used. This system is shown to be a statistical ensemble of nonrelativistic stochastic pointlike particles. The electron spin is shown to have a classical analog which is a collective (statistical) property of the ensemble (not a property of a single electron). The magnetic moment of the electron is a quantum property which has no classical analog. The (...) magnetic moment is parallel to the spin only in the stationary state. In the arbitrary state the magnetic moment is not connected with the spin direction. (shrink)

When observers view a rapidly moving stimulus they may see only a static streak. We report that there can be a transient percept of motion if such a moving stimulus is preceded or followed by a stationary image of that stimulus. A ring of dots was rotated so rapidly observers only saw a continuous outline circle and could not report its rotation direction. When an objectively stationary ring of dots preceded or followed this rotating ring, the stationary (...) ring appeared to visibly launch into motion from a standstill or visibly rotate to a halt, principally in the same direction as the actual rapid rotation. Thus, motions too rapid to be consciously perceived as motion can nonetheless be processed by the visual system, and generate neural transition states that are consciously experienced as motion percepts. We suggest such transition states might serve a unifying function by bridging discontinuous motion states. (shrink)

The tensorial relativistic quantum mechanics in (1+1) dimensions is considered. Its kinematical and dynamical features are reviewed as well as the problem of finding the Dirac spinor for given finite multivectors. For stationary states, the dynamical tensorial equations, equivalent to the Dirac equation, are solved for a free particle, for a particle inside a box, and for a particle in a step potential.

We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective cooperation pressures. To this end we generalise existing path-integral approaches to replicator systems with random asymmetric couplings. This technique allows one to formulate an effective dynamical theory, which is exact in the thermodynamic limit and which can be solved for persistent order parameters in a fixed-point regime regardless (...) of the symmetry of the interactions. The onset of instability can be determined self-consistently. We calculate quantities such as the diversity of the respective populations and their fitnesses in the stationary state, and compare results with data from a numerical integration of the replicator equations. -/- . (shrink)

This memoir consists of two parts, of which the first deals with the foundations of the theory of the struggle for existence, and begins with the introduction of the important concept of quantity of life, besides that of population. The fundamental equations are then established for the case where the individuals of a biological association mutually devour each other, the reasoning being based on the principle of encounters and on the fundamental hypothesis of the existence of equivalents of the individuals (...) constituting the different species which form the association.Having now obtained the equations which determine the rates of change of the numbers of individuals and of the quantities of life of the species, the memoir proceeds to find the equations relating to the stationary state, by establishing theorems which are afterwards applied for the purpose of obtaining the three general laws of the fluctuations. This investigation of the equilibrium state is then followed by the determination of the integrals of the fluctuation equations, and the deduction from these of their most important consequences.The second part of the memoir contains the enumeration and demonstration of the general laws of the struggle for existence, which flow from the discussion of the principles and the integrals obtained in the first part. In this way there is established a new sort of dynamics, demographic dynamics, which, though substantially different from the dynamics of material systems, is developed from an analogous point of view.The second part begins with the principle of the conservation of demographic energy, according to which there are two sorts of energy, one actual and one potential, which transform mutually the one into the other. This principle is the analogue of the principle of conservation of mechanical energy. It is followed by the enunciation of the three laws relating to the biological fluctuations, the experimental verification of which has been investigated by several naturalists. The success which has attended their efforts is well known.Everybody knows the importance ofHamilton's principle in mechanics and in all the domains of physical science. An analogous variation principle can be found in biology, and from it one can deduce the fluctuation equations in the canonical Hamiltonian form and also in the form of a Jacobian partial differential equation. Their integrals in involution from the subject next studied, and in this way are found cases where the integration is reducible to quadratures.Hamilton's principle leads to the principle of least action . There exists also in biology a closely related principle, which may be called the principle of least vital action. Its analytical form is such that it requires the existence of a true minimum, a state of affairs which does not always hold good in the analogous case in mechanics.Die Abhandlung besteht aus zwei Teilen: Der erste ist den Grundlagen der Theorie des Kampfes ums Dasein gewidmet. Man beginnt damit, neben der Bevölkerung die Menge des Lebens einzuführen, welche eine sehr wichtige Rolle spielt. Man geht dann dazu über, die Grundgleichungen für den Fall aufzustellen, in welchem die Individuen einer biologischen Assoziation sich gegenseitig auffressen. Man wendet das Prinzip der Begegnungen an und stützt sich auf die Grundhypothese der Existenz von Individuenäquivalenten der verschiedenen Arten, welche die Assoziation bilden.Wenn man die Gleichungen, welche die Variationen der Individuenzahlen und der Lebensmengen der Arten liefern, gefunden hat, so schreitet man zu den statischen oder Gleichgewichtsgleichungen fort und findet so die Theoreme, die man alsdann benutzt, um die drei allgemeinen Gesetze der Fluktuationen zu erhalten.Nach dem Studium des Gleichgewichtes geht man dazu über, die verschiedenen Integrale der Fluktuationengleichungen zu finden und zieht endlich aus ihnen die wichtigsten Folgerungen.Im zweiten Teile werden die allgemeinen Gesetze des Kampfes ums Dasein, welche aus der Diskussion der Prinzipien und der im ersten Teil gewonnenen Integrale stammen, ausgesprochen und bewiesen. Man baut so eine neue Dynamik auf: die demographische Dynamik, welche, obschon sie wesentlich verschieden von derjenigen der materiellen Systeme ist, sich nach einem analogen Gesichtspunkt entwickelt.Man beginnt in diesem zweiten Teil mit dem Prinzip der Erhaltung der demographischen Energie, nach welchem zwei Energien, die aktuelle und die potentielle, sich ineinander verwandeln. Wir haben hier eine Analogie zum Prinzip der Erhaltung der mechanischen Energie. Dann werden die drei Gesetze der biologischen Fluktuationen formuliert. Für sie haben verschiedene Naturforscher experimentelle Bestätigungen gesucht. Man kennt den Erfolg ihrer Bemühungen.Alle Welt kennt die Bedeutung des Prinzips vonHamilton in der Mechanik und in allen Gebieten der Physik. Man kann ein dem Variationskalkül analoges Prinzip in der Biologie finden. Aus ihm kann man die Fluktuationsgleichungen in der kanonischen Form vonHamilton und in der Gestalt einer Gleichung mit partiellen Differentialquotienten vonJacobi herleiten. Ihre Integrale bilden den Gegenstand der folgenden Studien. Man findet Fälle, in denen die Integration sich auf Quadraturen reduziert.Das Prinzip vonHamilton zieht das Prinzip der kleinsten Wirkung oder das Prinzip vonMaupertuis nach sich. Auch in der Biologie gibt es ein mit dem vorgenannten zusammenhängendes Prinzip, welches man das Prinzip der kleinsten vitalen Wirkung nennen kann. Seine analytische Form ist derart, dass es sich um ein wahres Minimum handelt, das im analogen Fall in der Mechanik nicht immer zutrifft. (shrink)

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions in (...) “equilibrium”, even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics. (shrink)

The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. (...) geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic. (shrink)

The notion of dynamical symmetry is discussed in the framework of the symplectic tomography scheme for the harmonic oscillator. The stationary states are shown to appear as solutions to eigenvalue equation for “classical” probabilities. All the probabilities describing the energy levels are constructed using dynamical-symmetry operators.

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie–Bohm and modified de Broglie–Bohm formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable (...) of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the ‘which-way’ information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie’s wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results. (shrink)

Wegner’s method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is illustrated by analyzing some (...) physical examples. (shrink)

Erwin Schrödinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics” or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived at his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen Bohr's atom model for example, as a structure in space—time, but instead, following (...) the lead of Einstein's 1905 theory of relativity, representing only empirically observable properties, such as the transition amplitudes between the stationary states of the atom. These amplitudes can be arranged in square arrays of numbers. In Heisenberg's scheme these arrays, and other like them, are combined according to certain rules that were later recognized by Max Born to be the rules of matrix multiplication. The whole scheme is abstract and mathematical, and avoids using any space—time picture of what is going on at the atomic level. Schrödinger, on the other hand, represented the electron in an atom by a cloudlike wave surrounding the nucleus. This is a space—time structure that, superficially at least, is more in line with the classical physical theories of the eighteenth and nineteenth centuries. -/- Niels Bohr invited Schrödinger to come to Copenhagen to present his ideas, and to discuss this subject with himself, Heisenberg, and others. Schrödinger arrived in Copenhagen on October 1st, 1926, and was immediately intensively engaged by Bohr and the others in a “debate” that lasted for days. Eventually, Schrödinger become ill, and was confined in Bohr's home to a bed, upon which Bohr sat, continuing the discussion. Schrödinger finally exclaimed “If all the quantum jumping is here to stay, then I am sorry that I ever became involved in quantum mechanics”. Bohr replied, “But we are glad that you did!”. (shrink)

The conditional probability interpretation of quantum gravity has been criticized for violating the constraints of the theory and also not giving the correct expression for the propagator. We have shown that following Page’s proposal of constructing an appropriate projector for the stationary state of a closed system, we can arrive at the correct expression for the propagator by using conditional probability rule. Also, it is shown that a unitary evolution of states of a subsystem at local level may (...) be a consequence of non-unitary projection of appropriate states at global level. (shrink)

In this paper, we analyse the simplest possible three-dimensional model of endogenous growth to account for the relationship between financial intermediation and economic growth. In our setting, households maximize an interim utility function and firms maximize profit. Households can save money only through banks which offer firms investment loans. We show that under very general assumptions, investments realized by firms depend not only on savings accumulated by banks but also on financial intermediation technology ϕ(θ). Using mathematical methods of dynamical systems, (...) we found stationary states of the system and study their stability. (shrink)

The electric dipole moments of elementary particles, atoms, molecules, and their connection to the electric susceptibility are discussed for stationary states. Assuming rotational invariance, it is emphasized that, for such states, only in the case of a parity and time-reversal-violating interaction can the considered particles exhibit a nonvanishing expectation value for the electric dipole moment.

The notion of antifragility, an attribute of systems that makes them thrive under variable conditions, has recently been proposed by Nassim Taleb in a business context. This idea requires the ability of such systems to ‘tinker’, i.e., to creatively respond to changes in their environment. A fairly obvious example of this is natural selection-driven evolution. In this ubiquitous process, an original entity, challenged by an ever-changing environment, creates variants that evolve into novel entities. Analyzing functions that are essential during (...) class='Hi'>stationary-state life yield examples of entities that may be antifragile. One such example is proteins with flexible regions that can undergo functional alteration of their side residues or backbone and thus implement the tinkering that leads to antifragility. This in-built property of the cell chassis must be taken into account when considering construction of cell factories driven by engineering principles. (shrink)

THIS paper seeks to elucidate the phenomenon known in psychology as 'the specious present,' by postulating a two-dimensional theory of the extensional aspects of time. On this theory, the usual logical and psychological difficulties, encountered in current accounts of this phenomenon, can be resolved. For, when there are two dimensions of time, the same event may be without extension in one of these dimensions ('transition-time'), while it is nevertheless finitely extended in the other of these dimensions ('phase-time'); so that in (...) a definable sense the phases of a finitely enduring event, though successive in one time-order, yet are contemporary in the other. The epistemological standpoint implicit in the paper is generally similar to the one Bertrand Russell has put forward, in his Physics and Experience (Cambridge, 1946), and his Human Knowledge: Its Scope and Limits (London, 1948) (allowing for the changes which would be required in Russell's theory to take into account a second time dimension). A 'psycho-neural parallelism,' or one-one correspondence, is postulated between features of certain 'experiential events' (namely, those experiential events normally held to be happening to some person's mind, which are describable in the language of psychology); and features of certain 'physical events' (namely, those events described in the language of physics, chemistry and physiology, which are ordinarily conceived as happenings in that same person's body). These physical events are conceived of as being causally connected with events in the physical world outside the experient's body, by means of the concepts of light waves, sound waves, chemical stimuli, and consequential processes in the nervous system (central and peripheral) and sense-organs, in the usual way. In terms of this psycho-neural parallelism the physical correlate of the finite temporal span of the specious, or experiential present, is to be found in certain consequences of the uncertainty principle in quantum physics; according to which there is a finite interval of time necessarily associated with a nearly precise determination of energy levels, and of transitions between them. Some of the physical implications of this theory, applied to processes in the material structure of the human body, are discussed qualitatively. But, for the reasons given in the last section of the paper, a quantitative treatment is not yet possible. The paper is greatly indebted in regard to the physical application of the two-dimensional theory of time, to the discussion of the pentadic group structure in Eddington's Fundamental Theory (Cambridge, 1946 and 1950); and in particular to the treatment there of the phase-variable as the 'time-analogue' in the quantum statistics of stationary states. (shrink)

The author proposes to show that the actual crisis in microphysics is principally due to the fact that, as quantum mechanics is a theory of stationary states and reversible movements, it fundamentally ignores the notion of a transitory process. The essential characteristic of quantum theories is the result of an evolution of more than two centuries; a period of development essentially devoted to the description of stationary and reversible phenomena. The author's point of view, which reflects that of (...) the school of Louis de Broglie, is that microphysics must now cross a new threshold in giving up the description of stationary states and the calculation of their transition probabilities in favor of attempting to describe the transitions themselves and explain the origin and stability of stationary states. The future seems to him to be one of a microphysics based on irreversibility. (shrink)